The result of the attempts to simplify the structure of the multiplet (on the left hand-side of the demonstration pages) obtained by the application of the inverse of the convolution with doublet of delta function (the effect of J) are measured for different splitting. The error functions are displayed on the right. The measure uses a scalar product calculated for the vectors formed by the multiplet obtained by simplification starting at either sides of the multiplet. It reaches the unit value when they are indentical. When running from the right side of the error function, the first extremum reaching a minimal level (typically 0.95) points to the larges coupling present in the multiplet.
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Refs. Papers by G. Bodenhausen’s group, in particular by P. Huber and D. Jeannerat.
In particular:
Jeannerat, D.; Bodenhausen, G. Determination of Coupling Constants by Deconvolution of Multiplets in NMR. Journal of Magnetic Resonance 1999, 141 (1), 133-140.
Peng, C.; Jeannerat, D.; Bodenhausen, G. Determination of Homonuclear Scalar Coupling Constants by Combining Selective Two-Dimensional NMR Spectroscopy with Convolution and Deconvolution: Applications to Paclitaxel (Taxol). Magnetic Resonance in Chemistry 1997, 35 (2), 91-99.
Jeannerat, D.; Bodenhausen, G. Accurate determination of passive coupling constants by analysis of complementary two-dimensional cross-peak multiplets. Journal of Magnetic Resonance. A 1996, 118 (1), 126-131.